BALL CONVERGENCE FOR A NOVEL-FOURTH ORDER METHOD FOR SOLVING SYSTEMS OF EQUATIONS
IOANNIS K. ARGYROS
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA.
Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, India.
*Author to whom correspondence should be addressed.
We present a local convergence analysis of an ecient iterative method free from second derivative in order to approximate a locally unique solution of a nonlinear equation F(x) = 0, where operator F : ℝm → ℝm. In earlier studies such as ,  the fourth order of the method was estabished under hypotheses reaching up to the fourth derivative although the method uses only the rst derivative. We expand the applicability of the method using only hypotheses on the rst derivative. A ball of convergence, error estimates on the distance involved and a uniqueness result are given using Lipschitz constants. Numerical examples are also presented in this study.
Keywords: Multi-point, multi-parametric method, chebyshev-halley methods, high convergence order, local or ball convergence, radius of convergence